It is estimated four fifths of passengers paying in cash do so because the balance on their Oyster cards has dropped below the cost of their journey.

Sweden is already moving towards scrapping cash completely on its public transport network.

Elsewhere in Britain, many major operators have already introduced smart cards, although moves to scrap cash completely a long way off.

Go Ahead, one of the country's largest bus operators, has introduced a card known as The Key, which is already used for three million journeys a month outside London.

It says the card, which is currently generating about 10 per cent of its revenue outside the capital, is in its infancy.

Smart cards are already used in various parts of the country including Oxfordshire.

Elsewhere in Plymouth, Brighton and Hove and parts of north east England, thousands of passengers are downloading tickets onto their mobile phones.

Stagecoach, another major operator, estimates 200 million of the 670 million journeys made on its buses every year are paid for with a smart card.

A Department for Transport spokesman said the Government supports the technology.

“Any move to cashless bus services in London, or elsewhere, is a matter for local decision makers. The Coalition Government recognises that smart ticketing offers real benefits to passengers by making buying and using tickets simpler.

''That is why we are actively encouraging smart ticketing roll-out to other areas of England.”